Trignometry Test

Result

Trignometry Test - 1

Score
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Rank
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TIME Taken - -

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Question 1
1 / -0

If cos⁴ θ + α, sin⁴ θ + α are the roots of the equation x² + b (2x + 1) = 0 and cos² θ + β, sin² θ + β are the roots of the equation x² + 4x + 2 = 0 then b is equal to

A
-2

B
-1

C
2

D
1

Solution

We have
cos⁴ θ - sin⁴ θ = cos² θ - sin² θ = cos2θ
⇒ (-2b)² - 4b = (-4)² - 4 × 2
⇒ b² - b - 2 = 0 ⇒ b = -1,2
Question 2
1 / -0

If sin α, sin β and cos α are in G.P. Then roots of the equation x² + 2x cot β + 1 = 0 are always

A
Equal

B
Imaginary

C
Greater than 1

D
Real

Solution

sin α, sin β, cos α are in G.P
⇒ sin² β = sin α cos α
⇒ cos 2β = 1 - sin 2α ≥ 0

Now the discriminant of the given equation is
4cot² β - 4 = 4 cos 2β. cosec² β ≥ 0
⇒ Roots are always real